Wow, what a wonderful treasure you have from your DGG. I think you have to do what feels right for you. I agree to check with either a quilt museum or someone who restores quilts for advise. Myself, I would finish it with batting in the middle and I would utilize my DGG's clothes to piece the backing, I would tie it off so as to not see the ties and hand sew the binding on both sides. Lucky you to have this precious quilt top.